# Reverberation Calculation

In theory, it is easy to determine the reverberation time of a room. It depends on the volume of the room and the rate at which the sound energy is absorbed by the wall surfaces and the objects in the room. In a bare room, the reverberation time is thus proportional to the ratio of volume to surface. It is customary to define the reverberation time as the time required for the sound level to decrease by 60 dB (hence the abbreviation RT60). In 1922 a pioneer in the study of room acoustics, Wallace Sabine came up with the formula which is used here by this calculator:

**RT60 = k(V/Sa)**

**k** is a constant that equals 0.161 when the units of measurement are expressed in meters and 0.049 when units are expressed in feet. **Sa** is the total surface absorption of a room expressed in sabins. It is a sum of all the surface areas in the room multiplied by their respective absorption coefficients. The absorption coefficients express the absorption factor of materials at given frequencies. **V** is the volume of the room.

I got this page and the following calculator from a page offered by the New York University education page. The author was Piotr Filipowski (Just trying to give credit where credit is due) Its Java script.

RT60 Calculator

Enter the measurements of your room. Make sure you specify the units.

**So what can we work out with this calculator?**

Let's start with a room with the following dimensions.

- Length 6 metres
- Width 5 metres
- Height 2.4 metres.

and with all the walls and ceiling in painted concrete and the floor in unpainted concrete. (i.e. we are going to treat the garage) We are then going to add the **typical treatment** (you know, get out the egg cartons, heavy drapes and curtains etc)

- Carpet on the floor
- Heavy drapes on the rear wall
- Heavy drapes on the front wall
- Light drapes (egg cartons) on the side walls
- Light drapes (egg cartons) on the ceiling.

The original room has a relatively flat response (Bright Blue), albeit a bit long all over and especially in the top end, and would sound very bright and live with reverb times around .8 sec. When the **typical treatment** is applied we land up with a room that has a long reverb time at 125Hz and short at 4kHz. Because the high end reverb is shorter people will say the room is dead but in fact it's not really, it's only dead in the top end and too dead at that. The frequencies below 500Hz are the real concern.

**This is the mistake everyone seems to make.** All the treatment added only effects the high frequencies. You must consider all the frequencies when you treat a room. The shorter reverberation time in the high end is reasonable at 0.3 sec (around 0.4 -0.5sec is desirable) but you must take down the low end as well. The reverb time at 125Hz is around 2 sec, at 250 it's 0.92 sec,at 500 it's down to 0.49 sec and it reaches 0.3 sec at 1000Hz and is right down to 0.21 sec at 4kHz. The low mid and lows need correct treatment.